Peeling approaches on simple networks. Core decomposition is a simple but effective model to locate the seed regions where dense subgraphs can be found [1]}.
It makes use of degrees to assign core numbers to nodes.
Regularizing the node degrees, that span to a large range, to the core numbers in a smaller range is the key and makes the peeling a fundamental building block in an array of applications [2]}, [3]}, [4]}, [5]}, [6]}.
Higher-order variants of the peeling are introduced to take advantage of the triangles and small subgraphs.
Truss decomposition leverages triangles [7]}, [8]}, [9]}, nucleus decomposition makes use of small cliques [10]}, [11]}, and tip/wing decomposition utilizes butterflies (\(2,2\) -bicliques) in bipartite networks [12]}, [13]} to find dense regions in a principled way.
Nucleus decomposition generalizes core and truss decompositions. It finds \(k\) -\((r,s)\)  nucleus, defined as a subgraph where each \(r\) -clique is a part of \(k\)  number of \(s\) -cliques where \(r<s\) .
Those peeling approaches work on undirected simple networks. Here we work on directed networks with attributes on nodes/edges.
We compare our methods with nucleus decomposition to highlight the benefit of considering edge directions and node labels.
